Helical model of compression and thermal expansion

A negative linear temperature expansion and a negative linear compressibility were observed for imidazolium benzoate salt. Its strongly anisotropic strain induced by the temperature and pressure changes has been explained by the mechanism of H-bonded helices deformed in the structure. X-ray diffraction and vibrational spectroscopy were used to analyze interactions in the crystal. The Quantum Theory of Atoms in Molecules (QTAiM) approach was applied to analyze the hydrogen bonds and other interactions. In the salt under study, the interactions within the helix are substantially higher in energy than between helices. With decreasing temperature and increasing pressure, the value of the helix pitch increases while the value of the semi-major axis decreases, which results in the negative linear expansion and negative linear compression, respectively.


Figure S1 .
Figure S1.ORTEP view of the molecules of salt BenImi (100 K), showing the atomic labeling schemes.Non-H atoms are drawn as 30% probability displacement ellipsoids, and H atoms are drawn as spheres of arbitrary size.

Figure S2 .
Figure S2.View of the unit cell of BenImi showing the layers of molecules parallel to the (1 ̅ 01) plane.Adjacent layers are shown in black and gray for clarity of drawing.The symmetry codes are explained in TableS2.

Figure S3 .
Figure S3.The helical structure in BenImi formed by anions and cations connected by NH···O hydrogen bonds (shown in green).

Figure S4 .
Figure S4.A room-temperature ion system at atmospheric pressure in BenImi, for which calculations were performed using QTAiM.The green dots correspond to bond critical points (BCPs).

Figure S5 .
Figure S5.Change in the angle between the anion and cation plane (θ) as a function of temperature (solid circles) and pressure (open circles).

Figure S7 .
Figure S7.Projection on the ab planes of the helix formed in the BenImi crystal structure at 300 K. Note: The total temperature-dependent change in the parameter a of an elementary cell is affected by changes in the semi-minor axis (bh) and changes in the distance between the helixes (denoted by X).The X value equals 1.097 Å (300 K) and 0.692 Å (100 K).The changes in this temperature range are X=0.40Å and bh= 0.05 Å.

Figure S8 .
Figure S8.The hydrogen bond network is shown in plan view (-8.62, -0.05, 2.12).Note: The blue arrows show the direction of ion movement as the temperature decreases, whereas the red arrow shows the movement of the carboxylate group.

Table S1 .
Crystal data, data collection, and structure refinement for BenImi at different temperatures at atmospheric pressure

Table S2 .
Crystal data, data collection, and structure refinement for imidazolium benzoate at different pressures at room temperature (T=293.02K).

Table S6 .
QTAiM parameters (in atomic unit) corresponding to the H•••O bond critical point (BCPs), the electron density at BCP ρBCP; Laplacian of electron density at BCP,  2 ρBCP; total electron energy density at BCP, HBCP and the components of the HBCP: kinetic electron energy density, GBCP; potential electron energy density, VBCP, the hydrogen bond energy, EHB.

Table S7 .
QTAiM parameters (in atomic unit) corresponding to the H•••O bond critical point (BCPs), the electron density at BCP ρBCP; Laplacian of electron density at BCP,  2 ρBCP; total electron energy density at BCP, HBCP and the components of the HBCP: kinetic electron energy density, GBCP; potential electron energy density, VBCP, the hydrogen bond energy, EHB.